In a Thursday night letter to CBS Corp.'s chief executive Leslie Moonves, Garcetti said that the city is "aggressively seeking to encourage more production here in Los Angeles by cutting red tape, lending proactive assistance, and by furthering public policy to compete with financial incentives offered by other states." (Emphasis added.)

The problem with Garcetti's proposal is that late-night talk shows don't qualify for film tax credits under California's current program. While a bill to expand film tax credits is in the state legislature, late night talk shows are not included.

But there may be efforts to change that.

Assembly member Mike Gatto (D-L.A.), one of the bill's joint authors, said he would consider adding language to the bill that would include shows like the "Late Show," but he expressed some reservations.

"I'm certainly open to considering something that would help foster the infrastructure necessary to attract a world class production like the 'Late Show,'" Gatto told KPCC, adding that he plans to huddle with his co-author, assembly member Raul Bocanegra (D-Pacoima).

Gatto said the legislature would need to be careful that it doesn't start to look like the government is selecting one favorite TV show or "one type of content over another."

"This tax credit, in order for it to work and for it to be supported by the people, it needs to show that it's going to help heal the industry as a whole and do so in a thoughtful way that is not just a way for the government to essentially pick winners and losers," Gatto said.

A CBS spokesman declined to comment.

Some industry leaders have blamed the low amount of tax credits as the reason for why TV and film production is leaving California for other states like New York. California offers $100 million in film tax credits a year, while New York offers roughly four times that amount.

A recent report by the Milken Institute found that California lost 16,137 film production jobs from 2004 to 2012, while New York gained 10,675 jobs in the same period.

New York has also done its own campaigning to keep the 'Late Show.' Melissa Mark-Viverito, speaker of the New York City Council, wrote a letter to CBS Corp.'s Moonves.

"New York has always been the home of the 'Late Show,' and nothing could be better for the future of the program than to continue in that tradition when the torch is passed to a new host," Mark-Viverito wrote in her letter.

Southern California is still reeling from the economic loss incurred when "The Tonight Show" moved to New York after 42 years in Southern California when Jay Leno retired and New York-based host Jimmy Fallon took over. There was a loss of more than 150 local NBC jobs, and many small businesses were hurt by the move.

Meanwhile, NBC benefited from it. When "The Tonight Show" moved to New York, NBC saved more than $20 million a year under the state's tax credit program because of new language that was added by the state legislature, according to the Associated Press.

In the future, Steve Dayan, chairman of the California Film Commission, said he would like the state's program to expand to productions like "Late Show." But the challenge is that the current level of incentives ($100 million in tax credits a year) is too low, he said.

"It’s literally gone in a day, so how can you think about even covering these types of productions?" Dayan asked.

Beyond financial incentives, Garcetti's spokesman Yusef Robb said there are many reasons why the "Late Show" should come to L.A.: The stars are based here, he said, and it's the "best city in America to do business now."

"Mayor Garcetti is committed to making filming here in Los Angeles, whether it's television or movies, as easy [and] as cost effective as possible. And the weather is great," he said.

Robb added that the mayor's office has looked into cutting costs and red tape for film productions in areas such as water and power bills and permitting.

Robb said it's "too early to say" if language will be added to the proposed assembly bill to allow late night talk shows to qualify for tax credits. But he added that the message is that "the mayor of the second-largest city in America ... is willing to work with you to bring your production here."

Previously in The Breakdown

The Breakdown explains what's behind Southern California business and economic news. It describes the effects the headlines have on you: whether you're an investor, a business owner, an employee, homeowner, consumer or just someone who wants to know how to save a buck.